Sensitivity analysis of 1-DoF equivalent mechanisms for the kinematic modelling of the knee

Prosthesis and orthosis design requires mathematical models that simulate the motion of human joints. These models should be topologically simple, should reproduce the anatomical motion with high accuracy and should have a high numerical stability. As for the knee joint, many one-degree-of-freedom models have been formerly proposed in order to achieve this target; in particular, two mechanisms proved to be interesting, both of them having their own peculiarities. The first one replicates the anatomical motion very well and the second one is very simple from a mechanical point of view, although slightly less accurate. Moreover, some indicators, such as the large difference between the time required by the identification procedure of the two mechanisms, led to suppose that the second model could have a higher numerical stability than the first one. In this context, high numerical stability is associated with three different properties of mechanisms: low sensitivity to geometrical parameter variation, low disposition to generate singularity problems and high regularity of motion. Numerical stability of both mechanisms was quantitatively assessed in this paper to verify the preliminary supposition, by analyzing all these aspects. The results proved that, as hypothesized, the second model performs better than the first one from this point of view. This characteristic, combined with the mechanical simplicity and the acceptable accuracy, makes the second model very interesting in many practical applications, as exoskeleton or prosthesis and orthosis design.